The present invention is generally related to a signal processing system for either a magnetic disk apparatus or an optical disk apparatus. More specifically, the present invention is directed to a high-efficiency demodulating method of a high-order partial response system such as an EEPRML (Extended Extended Partial Response Maximum Likelihood) signal processing system and an EEEPRML (Extended EEPRML) signal processing system.
In magnetic disk apparatuses, the partial response maximum likelihood (will be abbreviated as a xe2x80x9cPRMLxe2x80x9d hereinafter) signal processing system combining the partial response class 4 (PR4) and the maximum-likelihood decoding system are practically available as a high-efficiency signal processing system. A high-efficiency signal processing system implies a system capable of realizing a desirable data error rate at a low SIN (signal-to-noise) ratio. Very recently, such high order partial response systems have been practically utilized as signal processing systems capable of reproducing signals at SIN ratios lower than that of the PRML system, for instance, the EPRML system by combining the EPR4 (Extended PR4) with the maximum (most) likelihood decoding system.
FIG. 1 shows a structural example of the construction of a general magnetic disk apparatus using a PRML signal processing system. Original data is supplied to an error correcting encoder 7 through an interface circuit 8 so that the original data is added with redundant data necessary for error correction. Next, the original data added with redundant data is subjected by a data modulator 6 to modulation necessary for the PRML system and is recorded on a magnetic disk 3 by a magnetic head 4 through a recording/reproducing amplifier 5. A signal reproduced from the magnetic disk 3 is passed through the recording/reproducing amplifier 5 and then PRML-processed by a data demodulator 1. The demodulated data is error-corrected by an error correcting decoder 2 and is thereafter converted through the interface circuit 8 into the original data. The operation and the arrangement of this data modulator 6 and data demodulator 1 will now be explained in more in detail with reference to FIG. 2 indicating a relationship between a magnetic recording/reproducing system and a partial response system. A first description will now be made of process operations executed on the data recording side. The data outputted from the error correcting encoder 7 is penetrated through a precoder 9 constructed of a delay element and modulo (Mod. 2), and then is recorded via a recording amplifier S on a recording medium. This precoder 9 is employed so as to prevent erroneous propagation of data which is caused during the demodulating operation.
Next, a description will now be made of a processing operation on the reproducing side. The magnetization on the recording medium is reproduced as a waveform having a differential characteristic by the recording/reproducing head. PR4 may regard this differential characteristic as a differential system of (1xe2x88x92D). In this case, symbol xe2x80x9cDxe2x80x9d implies a 1-bit delay calculator. The reproduced waveform is supplied to the equalizer 10 so as to be equalized in such a manner that a response of the waveform becomes (1+D). As a result, a total transfer characteristic in the output of the equalizer becomes (1xe2x88x92D2). Thereafter, a data discrimination of the data is carried out in the maximum decoder 11. FIG. 3 represents a response of a regenerative isolated waveform (note that a step response will be simply referred to as an xe2x80x9cisolated waveformxe2x80x9d hereinafter) in the case that a step waveform is magnetically recorded. PR4 implies that the isolated waveform is regarded as a waveform enlarged to 2 time slots, as indicated in FIG. 3A. This waveform owns such a characteristic having (1+D). Also, as indicated in FIG. 3B, EPR4 implies that the isolated waveform is regarded as a waveform enlarged to 3 time slots. This waveform owns such a characteristic having (1+D)2. Furthermore, as indicated in FIG. 3C, EEPR4 implies that the isolated waveform is regarded as a waveform enlarged to 4 time slots. This waveform owns such a characteristic having (1+D)3.
While considering the EEPR4 system as an example, the high order partial response system will now be summarized.
A total transfer characteristic of EEPR4 constitutes (1xe2x88x92D)xe2x80xa2(1+D)3 as a product of a transfer characteristic of an isolated waveform and another transfer characteristic of a magnetic recording system. An impulse response of the EEPR4 system determined by this product is represented in FIG. 4. As apparent from a waveform xe2x80x9caxe2x80x9d shown in FIG. 4, an isolated waveform of EEPR4 owns amplitude characteristics (normalized ratio) of 1, 3, 3, 1 every bit period. As a consequence, as indicated in a waveform xe2x80x9cbxe2x80x9d of FIG. 4, a response of an isolated pulse is obtained by superimposing the isolated waveforms inverted along the upper/lower directions with each other by shifting a 1-bit time period. In other words, the response of the isolated pulse becomes 1, 2, 0, xe2x88x922, xe2x88x921. In FIG. 5, there is shown a trellis diagram of EEPRML obtained by combining a maximum likelihood decoder with EEPR4. As is well known in this field, the operation of the EEPRML system may be explained based upon the trellis diagram. In the drawing, symbol xe2x80x9cakxe2x80x9d indicates an input signal to EEPRML at a time instant xe2x80x9ckxe2x80x9d. In this case, reference numeral 12 indicates a state, and reference numeral 13 shows a state transition. An upper stage of a label (ak/yk) and a lower stage thereof indicate an input signal value and an output signal value, respectively. The states of the respective signal processing systems are determined by the past input signal series. In EEPRML, a level of a reproduction signal at the present time instant is influenced by signals over the past 4 time slots. Assuming now that a state at a time instant xe2x80x9ckxe2x80x9d is equal to xe2x80x9cskxe2x80x9d, it is given as
sk=((akxe2x88x924, akxe2x88x923, akxe2x88x922, akxe2x88x921)1ak(1,0)), and a total number of states becomes 16. At a time instant xe2x80x9ckxe2x88x921xe2x80x9d, state transitions originated from a plurality of states are collected to a specific state at the time instant xe2x80x9ckxe2x80x9d. With respect to these state transitions, a squared value of a difference between an output signal and an input signal, which are indicated at a low stage of each label, will be referred to as a xe2x80x9cbranch metricxe2x80x9d. Also, an accumulated value of branch metrics until the present time instant with respect to each of the states will be referred to as a xe2x80x9cpath metricxe2x80x9d. Among the state transitions collected to a specific-state at the time instant xe2x80x9ckxe2x80x9d, only such state transitions that a summation becomes a minimum value and this summation is made from path metrics until a time instant xe2x80x9ckxe2x88x921xe2x80x9d and branch metrics corresponding to the respective state transitions are selected as a state transition (path) capable of satisfying a maximum likelihood condition (most certain). This stage may be subdivided into the below-mentioned steps. In other words, the path metrics are added to the branch metrics (Add). Next, these added values are compared with each other every state, and such a state transition which becomes a minimum value is selected (Select). A series of these operations will be abbreviated as an xe2x80x9cACSxe2x80x9d. The maximum (most) likelihood decoding method is such well-known method that this ACS operation is repeatedly performed at each time instant and under each state, and then when the path metrics are finally converged onto one path on the trellis diagram, the data is determined.
The performance of EEPRML is determined by a minimum free distance (Dfree). In this case, xe2x80x9cDfreexe2x80x9d implies a minimum difference of path metrics among various sorts of combinations from a specific node to another specific node on the trellis diagram shown in FIG. 5. It is known that xe2x80x9cDfreexe2x80x9d of EEPRML is equal to 6. Furthermore, distances between signals subsequent to xe2x80x9cDfreexe2x80x9d become 8 and 10. These distances between signals of EEPRML are determined by a data pattern entered into the maximum likelihood decoder. In particular, a distance between-signals is defined by a continuous time at which a pattern is changed from 0 to 1, or from 1 to 0. As will be discussed later, assuming now that an inverting position contained in a pattern is expressed by, for example, xe2x80x9cpxe2x80x9d, in such a case that 2 sorts of patterns are set under 1-bit shifted condition, and these patterns own 3-time continuous inverting positions such as xe2x80x9cp+pxe2x80x9d, a distance between these patterns may give xe2x80x9cDfreexe2x80x9d. To further improve the performance of these EPRML system and EEPRML system, very recently, Maximum Transition Run Code (will be abbreviated as an xe2x80x9cMTR codexe2x80x9d, hereinafter) has been proposed.
For instance, the conventional MTR code is described in, for example, xe2x80x9cMaximum Transition Run Codes for Data Storage Systemsxe2x80x9d, IEEE Transactions on Magnetics, volume 32, No. 5, September 1996, pages 3992 to 3994. The above-described MTR code owns a function to restrict that inverting of a pattern occurs more than 3 times. When this MTR code is used, a limitation can be made to the pattern inversion for more than 10 distances between signals of EEPRML. As a consequence, an S/N ratio of a signal can be equivalently improved. However, in the MTR code, the code rate becomes 4/5 and the like. This code rate value is low, as compared with the normally used 16/17 GCR (Group Coded Recording) and 8/9 GCR. As a result, a code rate loss becomes large, and a total coding gain cannot be always satisfied. Concretely speaking, a gain becomes approximately 2.2 dB, since the distance between signals is improved-from 6 to 10. on the other hand, a code rate loss becomes larger than approximately 1 dB under normalized line density=3, for instance, (normalized line density=a half bandwidth of a reproduced waveform is normalized by a width of a recording pulse), and a total coding gain becomes at maximum approximately 1 dB, depending upon a recording density of a magnetic disk.
An object of the present invention is to provide a generally-used method for expanding the distance between signals of a high order partial response system, especially, the EEPRML system and the EEEPRML system irrespective of a code under use. In other words, an object of the present invention is to provide a method for equivalently expanding a distance between signals without newly producing a code rate loss, since the 16/17 GCR, or the 8/9 GCR used in the PRML signal process operation for a magnetic disk apparatus can be directly applied.
In accordance with the present invention, in the high order partial response system, especially the EEPRML system and the EEEPRML system, a response of an isolated pulse waveform is changed from the original response of EEPRML, or EEEPRML, so that the distance between signals can be expanded. In the high order partial response system, a response of an isolated pulse is selected to be an symmetrical waveform. For instance, as previously described, in the EEPRML system, the response of the isolated pulse waveform becomes 1, 2, 0, xe2x88x922, xe2x88x921.
In accordance with the present invention, since the asymmetrical characteristic owned by the response of the isolated pulse waveform in such a high order partial response system is relaxed, the distance between signals is firstly extended. This distance between signals determines the S/N ratio when the signal is discriminated. It is implied that the longer this distance between signals becomes, the larger the amplitude of the signal equivalently becomes. Secondly, the noise power is reduced. The noise of the partial response owns correlative relationships with each other over plural time instants. The performance of the maximum likelihood decoder is deteriorated by the adverse influence caused by this correlative relationship of the noise. As a result, the noise can be essentially reduced by suppressing the correlative characteristic of the noise. In other words, an S/N ratio of a high order partial response signal is defined by the following formula:
S/N=distance between signals/(noise powerxc3x97noise correlative coefficient)xe2x80x83xe2x80x83(1).
While considering the EEPRML system, the present invention will now be explained with a concrete example. A code is equal to a binary number of {1, 0}. Now, in order to defame a dimension of a code error, a value of 1 corresponds to such an error case that 1 erroneously becomes 0; a value of xe2x88x921 corresponds to such an error case that 0 erroneously becomes 1; and a value of 0 corresponds to such an error case that no error occurs. The error patterns of the EEPRML system are classified in accordance with this definition:
(A). In a case that the distance between signals=6 (1, xe2x88x921, 1).
(B). In a case that the distance between signals=8:
1) (1,xe2x88x921,1,0,0,1,xe2x88x921,1)
2) (1,xe2x88x921,1,xe2x88x921,1).
(C). In a case that the distance between signals=10: (0, 1, 0) etc.
An actual code error pattern of (A) is such a case that (a, b, 1, 0, 1, c, d) erroneously becomes (a, b 0, 1, 0, c, d), or vice versa.
An actual code error pattern of (B) 1) is such a case that (1, 0, 1, a, b, 1, 0, 1) erroneously becomes (0, 1, 0, a, b, 0, 1, 0), or vice versa.
An actual code error pattern of (B) 2) is such a case that (1, 0, 1, 0, 1, 0, 1) erroneously becomes (0, 1, 0, 11 0, 1), or vice versa. In this case, symbols xe2x80x9caxe2x80x9d, xe2x80x9cbxe2x80x9d, xe2x80x9ccxe2x80x9d, and xe2x80x9cdxe2x80x9d are arbitrary.
(C) is a 1-bit isolated pulse error.
As previously described, with respect to the patterns commonly applied to (A) and (B), the signals are inverted at least 3 times. As a consequence, in the data pattern, either xe2x80x9cab1010cdxe2x80x9d or xe2x80x9cab0101cdxe2x80x9d, and also these data patterns are continued. FIG. 6 represents that the error of the distance between signals=6 is plotted on a trellis diagram. Two sorts of data streams xe2x80x9cxcex1xe2x80x9d and xe2x80x9cxcex2xe2x80x9d, shown in FIG. 6 own such values of xe2x80x9c010abcdexe2x80x9d and xe2x80x9c101abcdexe2x80x9d. That is, only 3 bits thereof are different from each other. FIG. 7 indicates waveforms corresponding to these data streams. As apparent from this drawing, a distance between signals of the two sorts of patterns is 6. Similarly, FIG. 8 represents a waveform corresponding to the above-described (B) 1).
On the other hand, EEPRML has a transfer characteristic of (1xe2x88x92D)xe2x80xa2(1+D)3. As a result, as illustrated in the waveform xe2x80x9cbxe2x80x9d of FIG. 4, an impulse response is determined by 1, 2, 0, xe2x88x922, xe2x88x921. Therefore, in the case that a 1-bit error happens to occur, a distance between signals for the erroneous pattern and the pattern originally having no error becomes 10, namely equal to a squared summation of the respective values of this impulse response. This distance between signals is equal to energy itself owned by this impulse signal. As a consequence, the reason why there is such a pattern of the distance between signals=6, or the distance between signals=8, as indicated in FIG. 7 and FIG. 8 is given as follows. That is, a combination of these patterns is to cancel the energy owned by the original impulse signal. In other words, the EEPRML system involves such a pattern that an erroneous propagation readily occurs. A further consideration will now be made of the cause why such a distance between signals is decreased with reference to a waveform diagram shown in FIG. 9A and an impulse response indicated in FIG. 9B. This diagram shows a pattern whose distance between signals becomes 6 in EEPRML indicated in FIG. 7. In this pattern, as shown in FIG. 9A, inverting of the signal is continued 3 times, namely P1, P2, P3. As a result, as indicated in FIG. 9B(a), isolated waveforms having responses 1, 3, 3, 1 are alternately repeated in such a manner of positive-negative-positive. As a consequence, such a response of 1, 2, 1, 1, 2, 1 is obtained, and energy of-this signal becomes a squared summation of the respective values, namely (1)2+(2)2+(1)2+(1)2+(2)2+(1)2=12. On the other hand, signal energy of each of isolated waveform single body becomes (1)2+(3)2+(3)2+(1)2=20. Accordingly, in such a pattern that inverting of signals is continued 3 times, namely P1, P2, P3, a total signal energy of the 3 isolated waveforms, i.e., 60 is reduced to 12. For example, as shown in FIG. 9B(b), when the response of the isolated waveform having the amplitude of 1 located at the right end is eliminated from the responses of the isolated waveforms, the distance between signals may be increased up to 15. This implies that since the responses 1, 3, 3, 1 of the isolated waveforms in EEPRML are excessively extended to a plurality of bits, the original energy of the signal is canceled in the specific patterns shown in-the above-described (A) and (B). This reason may cause the distance between signals to be essentially reduced. As a result, the erroneous propagation is induced.
Based upon this consideration, the essential aspect in order to enlarge the distance between signals is to establish a measure how to concentrate energy without losing the energy (electric power) of the isolated waveform. In general, as shown in FIG. 10, a means for concentrating energy of a signal an isolated waveform is filtered by an all-pass filter 14 to satisfy a minimum, phase transition condition, which could be cleared based on the communication theory. In this case, a minimum phase transition condition implies that a zero point and a pole of a transfer function of a signal given by a rational function are present within the same unit circumference. Since a phase filter is set so as to satisfy this condition, energy of a signal can be concentrated to a front half portion of an impulse response while the energy of this signal is reserved. In a magnetic recording operation, it is well known that an isolated waveform can be approximated by way of the Lorentz waveform. When this is given by L(t), it is expressed by the below-mentioned formula (2):
L(t)=1.0/(1+(2t/TW)2)xe2x80x83xe2x80x83(2)
where symbol xe2x80x9cTWxe2x80x9d gives a half bandwidth.
As apparent from this formula (2), L(t) is a symmetrical waveform with respect to right/left directions. In this case, a ratio (TW/T) of a half bandwidth to a time width T of a pulse to be recorded is defined as a normalized line density. When the value of this ratio TW/T is increased, the waveform may be recorded in the high density. Normally, in the magnetic recording operation, such a Lorentz waveform whose normalized line density is selected to be approximately 2.5 is used. It is now assumed that waveforms produced by filtering a Lorentz waveform having a normalized line density of 2.5 and another Lorentz waveform having a normalized line density of 3.0 by a minimum phase transition filter is recognized as L min(t), FIG. 11 indicates L min(t). As apparent from FIG. 11, the waveforms are symmetrical with each other along the right/left directions. Also, it can be understood that the energy is concentrated to the front half portion of the isolated waveform. However, generally speaking, it is very difficult to extract a clock signal (timing signal) required to discriminate a signal from an asymmetrical waveform. As one of these reasons, a jitter component (temporal fluctuation) depending upon a pattern is increased due to a phase distortion. As another reason, since the signal amplitude has multi-values, the clock signal (timing signal) extracting circuit becomes complex. This practical reason makes it difficult. As a consequence, according to the present invention, in order to solvexe2x80x94this contradictory condition, the polynomial PR(D) of the high order partial response is factorized in accordance with the following formula (3):
PR(D)=(1xe2x88x92D2)xe2x80xa2(C0+C,D+ . . . +CnDn)xe2x80x83xe2x80x83(3)
The above-described asymmetric characteristic is given to the waveform by such a manner that the timing extraction is carried out under condition of a front term in a right hand, and thereafter an asymmetrical response given by a rear term in the right hand is given by the discrete time filter. At this time, a selection is made of such asymmetrical coefficients C0, C1, Cn that the S/N ratio given by the formula (1) becomes maximum.
Next, a description will now be made of an actual method for calculating the asymmetrical coefficients. In a first case of 16 states in EEPRML, the above-explained asymmetrical coefficients are given as (C0=1, C1=2, C2=1). In other words, the value of C0 and the value Of C2 constitute symmetrical coefficients, while setting C1 as a center. To the contrary, in order to calculate the asymmetrical coefficient, first of all, a rear term of a right hand of the formula (3) is set as mornic polynomial of C0=1. Assuming now that the coefficients C1 and C2 are regarded as 2 variable functions of a real number, an optimum coefficient is calculated in accordance with the evaluation basis of the formula (1). Therefore, an integer coefficient most approximated to this real number is calculated. It should understood that since the methods for calculating the distance between signals, the noise power, and the noise correlative coefficient indicated in the formula (1) are described in detail in the publication xe2x80x9cMaximum Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interferencexe2x80x9d, IEEE Transactions on Information Theory, vol. IT-18, No. 3, May 1972, pages 363 to 378, descriptions thereof are omitted. A table 1 represents a typical characteristic of such a partial response that a state number thereof is 16. A distance of an isolated pulse indicated in this table 1 is directly equal to electric power owned by the isolated pulse itself. A minimum distance corresponds to such minimum distance among distances on a trellis diagram of partial response signal having given coefficients. As a consequence, a distance of the minimum distance/isolated pulse may constitute an index for there is a particular improvement in the characteristic. It should also be noted that the characteristics of the table 1 and the table 2 correspond to such a case that the normalized line density is 2.5. Furthermore, according to the present invention, not only the S/N ratio can be improved, but also the length of the code error can be improved, as compared with the long continued errors caused by the conventional EEPRML and EEEPRML systems. That is, giving the utilization efficiency of the energy of the partial response for giving this distance. The partial response system having the coefficient according to the present invention may have the advantages as to this point, as compared with that of the normal EEPRML. As a result, it can be seen that the S/N can be effectively improved with respect to the EEPRML having the symmetrical coefficient. A table 2 represents a typical characteristic of such a partial response that a state number thereof is 32. Also, in this case, according to the present invention, the major error bit length is the 1-bit error bit length, or the 3-bit error bit length. As a consequence, the present invention has such a feature that the error correction can be effectively performed by combining with the error correction code having the code error correcting capability with respect to at least the 1-bit continuous error, and the 3-bit continuous error.